[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-266994-105":59,"doc-detail-266994-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","grammar-heros-reference-sheet-math-reference-formulas","Grammar Hero’s Reference Sheet - Math Reference Formulas","","Grammar Hero’s Reference Sheet provides a compact math formula and rule summary covering coordinate geometry and algebra topics. It includes slope, quadratic formula, equation forms, distance, midpoint, triangle angle sum, Pythagorean theorem, and triangle area, followed by linear equations and practical geometry. Additional sections cover simple interest, PEMDAS order of operations, perimeter, rate-time-distance, percent change, statistics measures, circle formulas, unit conversions, polygons, multiplication rules, quadrilateral perimeter and area.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/grammar-heros-reference-sheet-math-reference-formulas/266994/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/grammar-heros-reference-sheet-math-reference-formulas/266994.png","ImageObject",300,407,{"name":92,"@type":93},"Ben Jamin","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-09-14",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",22,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What are the key formulas for coordinate geometry in this sheet?","Question",{"text":113,"@type":114},"It lists slope of a line, quadratic formula, standard/slope-intercept/point-slope forms, distance between points, and the midpoint formula. It also provides triangle angle sum and area relationships.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How do you use PEMDAS when simplifying expressions?",{"text":118,"@type":114},"Perform operations in the order: parentheses, exponents, multiplication/division (left to right), and addition/subtraction (left to right). Multiplication and division share equal precedence, as do addition and subtraction.",{"name":120,"@type":111,"acceptedAnswer":121},"What geometry and unit-conversion topics are covered?",{"text":122,"@type":114},"The sheet includes circle formulas (area, circumference, diameter), perimeter and area rules for common quadrilaterals, polygon interior-angle sums, and tables for converting between units such as length, capacity, weight, and time.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},266994,1789413847,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":130,"read_time":145},2336478466772,"https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2","Grammar Hero’s Reference Sheet  \n\n| Slope of a Line |\n| --- |\n| Let (x1, y1) and (x2, y2) be two points on the line.\u003Cbr>Slope = m = cchhaannggeeiinnyx = 􀯬􀯫22−~~ ~~􀯬􀯫11 |\n\n\n| Quadratic Formula |  |\n| --- | --- |\n| 􀝔 = | −􀜾 ± √􀜾2 − 4􀜽􀜿\u003Cbr>2􀜽 |\n| Note: ax2 + bx + c = 0 and a ≠ 0 |  |\n\n\n| Equations of Lines |\n| --- |\n| Standard Form: Ax + By = C\u003Cbr>Slope-Intercept Form: y = mx + b\u003Cbr>where m = slope and b = y – intercept\u003Cbr>Point-Slope Form: y – y1 = m (x – x1) |\n\n\n| Distance Formula |\n| --- |\n| 􀝀 = √(􀝔2 − 􀝔1)2 + (􀝕2 − 􀝕1)2\u003Cbr>d = distance between points (x1, y1) and (x2, y2) . |\n\n\n| Midpoint Formula |\n| --- |\n| 􀜯 = (􀝔~~ ~~1~~ ~~+2~~ ~~􀝔~~ ~~2 , 􀝕~~ 1 ~~+2~~ ~~􀝕~~ 2 ~~ )\u003Cbr>M = point halfway between points (x 1, y1) and (x2, y2) . |\n\n\n| Triangle Sum Theorem |\n| --- |\n| The sum of the three interior angles in a triangle is always 180°: ∠a + ∠b + ∠c = 180°\u003Cbr>|\n\n\n| Pythagorean Theorem |\n| --- |\n| In any right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse: a2 + b2 = c2\u003Cbr>|\n\n\n| Area of a Triangle |\n| --- |\n| 􀜣 = 12 􀜾ℎ |\n| |\n| b = the base of any triangle h = perpendicular height of any triangle |\n\nCopyright © 2020 by Grammar Hero Tutoring. This reference sheet is for personal use only. Unauthorized replication, especially for commercial purposes, is strictly prohibited. All rights reserved. Grammar Hero’s YouTube Channel  \n\n| Simple Interest Formula |\n| --- |\n| 􀜫 = 􀝌􀝎􀝐\u003Cbr>p = Principal (i.e., loan or investment amount) I = Interest earned\u003Cbr>r = Rate of interest per year in decimal form t = Time in terms of years |\n\n\n| Order of Operations (PEMDAS) |\n| --- |\n| Order of operations refers to the order in which calculations are performed to evaluate an expression. The acronym PEMDAS is useful for remembering it.\u003Cbr>P Parenthesis E Exponents MD Multiplication and Division (Left to Right) AS Addition and Subtraction (Left to Right)\u003Cbr>Note: Multiplication and division have equal precedence, so their calculations are performed as they appear in the expression from left to right. Likewise, addition and subtraction have equal precedence, so their calculations are performed as they appear from left to right. |\n\n\n| Perimeter |\n| --- |\n| To find the perimeter of any polygon, excluding circles, you simply add up all of its sides. For example:\u003Cbr>\u003Cbr>Note: The perimeter of a circle is its circumference. |\n\n\n| Distance, Rate, and Time Formula |\n| --- |\n| 􀝀 = 􀝎􀝐\u003Cbr>d = distance, r = rate\u003Cbr>t = time\u003Cbr>Rate and time must be in proportional units (e.g., if rate is given in terms of miles per hour, time must be in terms of hours) |\n\n\n| Percent Change |  |  |\n| --- | --- | --- |\n| 􀜲􀜥 = | 􀜰􀝁􀝓 􀜸􀜽􀝈􀝑􀝁 − 􀜱􀝈􀝀 􀜸􀜽􀝈􀝑􀝁􀜱􀝈􀝀 􀜸􀜽􀝈􀝑􀝁 | 􀝔 100 |\n| PC = Percent Change\u003Cbr>If PC is positive, there was an increase. If PC is negative, there was a decrease |  |  |\n\n\n| Statistics |\n| --- |\n| 􀛻􀜍􀜉􀜖 = Sum~~ ~~ofNumberallofDDataataPPooiintsnts\u003Cbr>Range = Maximum Value – Minimum Value\u003Cbr>Mode = The value in the data set that occurs the most often\u003Cbr>Median = The value in the middle of the data set\u003Cbr>To find the median of a data set, arrange the observations in order from smallest to largest value. If there is an odd number of observations, the median is the middle value. If there is an even number of observations, the median is the average of the two middle values. |\n\nCopyright © 2020 by Grammar Hero Tutoring. This reference sheet is for personal use only. Unauthorized replication, especially for commercial purposes, is strictly prohibited. All rights reserved. Grammar Hero’s YouTube Channel  \n\n| Circles |\n| --- |\n| Area of a Circle: Circumference of a Circle: r = radius of a circle\u003Cbr>􀜣 = π􀝎2 􀜥 = π􀝀 or 􀜥 = 2π􀝎 d = diameter of a circle\u003Cbr>π = 3.14 or 22/7\u003Cbr>|\n\n\n| Converting Units |  |\n| --- | --- |\n| Larger unit → smaller unit | Multiply |\n| Smaller unit → Larger unit | Divide |\n\n\n| Linear Units |  |\n| --- | --- |\n| 12 inches (in) | 1 foot (ft) |\n| 3 feet | 1 yard (yd) |\n| 36 inches | 1 yard |\n| 63,360 inches | 1 mile (mi) |\n| 5,280 feet | ","cbCaiv0PZvbQCMlm","https://ap.wps.com/l/cbCaiv0PZvbQCMlm","pdf",571311,18,"English","# Slope of a Line\n# Quadratic Formula\n# Equations of Lines\n# Distance Formula\n# Midpoint Formula\n# Triangle Theorems\n# Pythagorean Theorem\n# Area of a Triangle\n# Simple Interest Formula\n# Order of Operations (PEMDAS)\n# Perimeter\n# Distance, Rate, and Time Formula\n# Percent Change\n# Statistics\n# Circles\n# Converting Units\n# Linear Units\n# Capacity\n# Weight and Mass\n# Time\n# Polygons\n# Multiplication Rules\n# Quadrilaterals","[{\"question\":\"What are the key formulas for coordinate geometry in this sheet?\",\"answer\":\"It lists slope of a line, quadratic formula, standard/slope-intercept/point-slope forms, distance between points, and the midpoint formula. It also provides triangle angle sum and area relationships.\"},{\"question\":\"How do you use PEMDAS when simplifying expressions?\",\"answer\":\"Perform operations in the order: parentheses, exponents, multiplication/division (left to right), and addition/subtraction (left to right). Multiplication and division share equal precedence, as do addition and subtraction.\"},{\"question\":\"What geometry and unit-conversion topics are covered?\",\"answer\":\"The sheet includes circle formulas (area, circumference, diameter), perimeter and area rules for common quadrilaterals, polygon interior-angle sums, and tables for converting between units such as length, capacity, weight, and time.\"}]","Grammar Hero’s Reference Sheet - Math Reference Formulas | PDF",45]